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A168804
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Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
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1
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1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000
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OFFSET
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0,2
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COMMENTS
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The initial terms coincide with those of A170750, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 12010035158999999999999999535, A170750(19) = 12010035159000000000000000000. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
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FORMULA
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G.f.: (t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
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MATHEMATICA
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CoefficientList[Series[(t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2016 *)
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CROSSREFS
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Cf. A170750 (G.f.: (1+x)/(1-30*x)).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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